Group-invariant solutions of kinetic equations
type: Item
instance of: scholarly article
title: Group-invariant solutions of kinetic equations
zbMATH Open document ID: 0536.76073
DOI: 10.1007/BF01090031
author: A. I. Bunimovich
author: A. V. Krasnoslobodtsev
published in: Fluid Dynamics
publication date: 1983-01-01T00:00:00Z
review text: Similarity solutions of the Bhatnagar-Gross-Krook equation of kinetic theory are obtained by group theoretic methods. Solutions f depending on space x, time t, and velocity v are sought by rewriting the equations as an infinite system of partial differential equation in x and t for the moments \(f_ k\) of f with respect to v. This system is reduced to an infinite system of ordinary differential equations for the similarity solutions. By the group theoretic method various possible similarity forms are found and in several special cases the full distribution function or some of its moments are constructed explicitly. The generalization of this method to the B-G-K equation with a variable cross section and to the full Boltzmann equation are outlined.
Mathematics Subject Classification ID: 76P05
Mathematics Subject Classification ID: 82B40
Mathematics Subject Classification ID: 45K05
zbMATH DE Number: 3852672
zbMATH Keywords: full distribution function or moments
zbMATH Keywords: Similarity solutions
zbMATH Keywords: Bhatnagar- Gross-Krook equation
zbMATH Keywords: group theoretic methods
zbMATH Keywords: variable cross section
zbMATH Keywords: Boltzmann equation
MaRDI profile type: Publication
cites work: Q4135140
cites work: Q4135146
cites work: Exact solutions of the Boltzmann equation
cites work: Q3943693
cites work: Q4188958
description: scientific article; zbMATH DE number 3852672